={Ke−3x−2y0

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose the JPDF of X, Y is

f(x,y)={Ke−3x−2y0<x,x<y0otherwisef(x,y)={Ke−3x−2y0<x,x<y0otherwise give clear working of the following questions.

i) Find K so that f(x,y)f(x,y) is a valid jpdf.

 

       For correct value of K, so that f(x,y)f(x,y) is a valid jpdf;

ii)    Find E[X]E[X],

iii)   Find E[Y]E[Y],

iv)   Find E[XY]E[XY]

v)   Find Cov[X,Y]Cov[X,Y]

vi)    Are the random variables X and Y are independent? Why or why not?

Also use the working in this question to answer the following five questions.

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